Question

16. Determinaţi mulţimile:
a) A = {n € N[ 1 < √n <2};
N | 3 < √√n ≤ 4};
c) C = {ne
b) B = {n € N [ 2 ≤ √n <3};
d) D = {n € N ] 4 ≤ √n ≤5}.

Answer 1

Răspuns:

Explicație pas cu pas:

Answer 2

$\it a)\ \ 1 < \sqrt n < 2 \Rightarrow 1^2 < (\sqrt n)^2 < 2^2 \Rightarrow 1 < n < 4 \Rightarrow A=\{2,\ \ 3\}\\ \\ \\ b)\ \ 2\leq\sqrt n < 3 \Rightarrow 2^2\leq(\sqrt n)^2 < 3^2 \Rightarrow 4\leq n < 9 \Rightarrow A=\{4,\ \ 5,\ \ 6,\ \ 7,\ \ 8 \}\\ \\ \\ c)\ \ 3 < \sqrt n\leq4 \Rightarrow 3^2 < (\sqrt n)^2\leq4^2 \Rightarrow 9 < n\leq16 \Rightarrow A=\{10,\ 11,\ 12,...,\ 16\}$